jrdunaway said:
Homework Statement
Solve for X
Homework Equations
x^2 + x + 1 > 2The Attempt at a Solution
x2 + x - 1 > 0
(x + 2)(x - 1/2) > 0
x > 2
x > 1/2
Wolfram Alpha said that the solutions for X are:
x>1/2 (sqrt(5)-1)
and
x<1/2 (-1-sqrt(5))
what did I do wrong?
Well, for one thing, your factorisation of x
2 + x - 1 to (x + 2)(x - 1/2) is wrong.
You can see that by multiplying those factors together. They won't equal the original quadratic.
What's the discriminant of the quadratic?
The other error is in supposing that, if AB > 0, then A > 0 and B > 0 is the only solution. Don't forget that A < 0 and B < 0 is also a valid solution. Remember, if you multiply two negative numbers together, you get a positive.
Another mistake was going from x + 2 > 0 to x > 2. Shouldn't that be x > -2?
The last mistake was in the way you expressed your solution. Even though you considered the A > 0 and B > 0 case, you wrote the solution as x > 2, x > 1/2. Remember the "AND" condition. If x > 2 AND x > 1/2, you should simply "collapse" that solution to x > 2 (the bigger value) since everything that's bigger than 2 is also bigger than 1/2. Of course, 2 and 1/2 are wrong values for this question (as I mentioned earlier), but I'm using them to demonstrate the concept for you.